Category: Arithmetic

Question Number 82019 by M±th+et£s last updated on 17/Feb/20 Answered by mind is power last updated on 18/Feb/20 $$2F1(k+1,k+1;k+2;1)=(k+1){\int }_0^1{x}^k{(1-x)}^{-k-1}dx$$$${not}\:{defind}\:{sir}\:{tchek}\:{this}\:{Quation}…

Question Number 147493 by henderson last updated on 21/Jul/21 $$\mathbf{hi},\mathbf{dears}\mathbf{masters}!$$$$\mathbf{A}=\{\mathit{a}\mathit{u}+\mathit{b}\mathit{v},(\mathit{a},\mathit{b},\mathit{u},\mathit{v})\in {\mathbb{Z}}^4\}\mathbf{with}\mathit{a}\ne \mathit{b}.$$$$1.\mathbf{prove}\mathbf{that}\mathbf{A}\mathbf{is}\mathbf{ideal}\mathbf{of}\mathbb{Z}.$$$$2.\mathbf{let}\mathit{\lambda }\mathbb{Z}=\{\mathit{\lambda }\mathit{n},\mathit{n}\in \mathbb{Z}\}.$$$$\mathbf{prove}\mathbf{that}\mathbf{A}\mathbf{has}\mathbf{a}\mathbf{smaller}\mathbf{element}\mathit{\lambda }\mathbf{strictly}$$$$\mathbf{positive}\mathbf{such}\mathbf{that}\mathbf{A}=\mathit{\lambda }\mathbb{Z}.$$$$3.\mathbf{prove}\mathbf{that}\mathit{\lambda }=\mathbf{gcd}(\mathit{a},\mathit{b}).$$…

Question Number 81836 by M±th+et£s last updated on 15/Feb/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 147334 by Tawa11 last updated on 19/Jul/21 $$\mathrm{If}{\log }_{6}30=\mathrm{a},{\log }_{15}24=\mathrm{b},\mathrm{evaluate}:{\log }_{12}60$$ Commented by otchereabdullai@gmail.com last updated on 20/Jul/21 $$\mathrm{nice}!$$…

Question Number 147252 by mathlove last updated on 19/Jul/21 Answered by Olaf_Thorendsen last updated on 19/Jul/21 $$l={(\frac{1}{5}+{(\frac{1}{5}+{(\frac{1}{5}+\dots )}^2)}^2)}^2$$$$l={(\frac{1}{5}+l)}^2$$$${l}^{\mathrm{2}} −\frac{\mathrm{3}}{\mathrm{5}}{l}+\frac{\mathrm{1}}{\mathrm{25}}\:=\:\mathrm{0} \…